Bayesian ordinal regression for multiple criteria choice and ranking

We propose a novel Bayesian Ordinal Regression approach for multiple criteria choice and ranking problems. It employs an additive value function model to represent indirect Decision Maker's (DM's) preferences in the form of pairwise comparisons of reference alternatives. By defining a likelihood for the provided preference information and specifying a prior of the preference model, we apply the Bayesian rule to derive a posterior distribution over a set of all potential value functions, not necessarily compatible ones. This distribution emphasizes the potential differences in the abilities of these models to reconstruct the DM's pairwise comparisons. Hence a distinctive character of our approach consists of characterizing the uncertainty in consequence of applying indirect preference information. We also employ a Markov Chain Monte Carlo algorithm, called the Metropolis-Hastings method, to summarize the posterior distribution of the value function model and quantify the outcomes of robustness analysis in the form of stochastic acceptability indices. The proposed approach's performance is investigated in a thorough experimental study involving real-world and artificially generated datasets. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a novel Bayesian Ordinal Regression approach for multiple criteria choice and ranking problems. The approach utilizes an additive value function model to represent the Decision Maker's preferences in the form of pairwise comparisons. It applies the Bayesian rule to derive a posterior distribution over potential value functions and employs the Metropolis-Hastings method for summarizing the distribution and conducting robustness analysis.